A string is stretched between fixed points separated by \(75.0~\text{cm}\). It is observed to have resonant frequencies of \(420~\text{Hz}\) and \(315~\text{Hz}\). There are no other resonant frequencies between these two. The lowest resonant frequency for this string is:
1. \( 155 \mathrm{~Hz} \)
2. \( 205 \mathrm{~Hz} \)
3. \( 10.5 \mathrm{~Hz} \)
4. \( 105 \mathrm{~Hz}\)

The coefficient of performance of a refrigerator is \(5.\) If the temperature inside the freezer is \(-20^\circ \text{C},\) the temperature of the surroundings to which it rejects heat is:
1. \(31^\circ \text{C}\)
2. \(41^\circ \text{C}\)
3. \(11^\circ \text{C}\)
4. \(21^\circ \text{C}\)

A photoelectric surface is illuminated successively by the monochromatic light of wavelength \(\lambda\) and \(\frac{\lambda}{2}\). If the maximum kinetic energy of the emitted photoelectrons in the second case is \(3\) times that in the first case, the work function of the surface of the mineral is:
[\(h\) = Plank’s constant, \(c\) = speed of light]
1. \(\frac{hc}{2\lambda}\)
2. \(\frac{hc}{\lambda}\)
3. \(\frac{2hc}{\lambda}\)
4. \(\frac{hc}{3\lambda}\)

In an astronomical telescope in normal adjustment, a straight line of length \(L\) is drawn on the inside part of the objective lens. The eye-piece forms a real image of this line. The length of this image is \(l.\) The magnification of the telescope is:
1. \(\frac{L}{l}+1\)
2. \(\frac{L}{l}-1\)
3. \(\frac{L+1}{l-1}\)
4. \(\frac{L}{l}\)

Two slits in Young’s experiment have widths in the ratio of \(1:25\). The ratio of intensity at the maxima and minima in the interference pattern \(\frac{I_{max}}{I_{min}}\) is:
1. \(\frac{9}{4}\)
2. \(\frac{121}{49}\)
3. \(\frac{49}{121}\)
4. \(\frac{4}{9}\)

Water rises to height '\(h\)' in a capillary tube. If the length of capillary tube above the surface of the water is made less than \('h'\), then:

Two vessels separately contain two ideal gases \(\mathrm{A}\) and \(\mathrm{B}\) at the same temperature, the pressure of \(\mathrm{A}\) being twice that of \(\mathrm{B}\). Under such conditions, the density of \(\mathrm{A}\) is found to be \(1.5\) times the density of \(\mathrm{B}\). The ratio of molecular weight of \(\mathrm{A}\) and \(\mathrm{B}\) is:

A circuit contains an ammeter, a battery of \(30~\text{V}\), and a resistance \(40.8~\Omega\)$$ all connected in series. If the ammeter has a coil of resistance \(480~\Omega\)$$ and a shunt of \(20~\Omega\)$$, then the reading in the ammeter will be:
1. \(0.5~\text{A}\)
2. \(0.02~\text{A}\)
3. \(2~\text{A}\)
4. \(1~\text{A}\)

The value of the coefficient of volume expansion of glycerine is \(5\times10^{-4} \mathrm{~K^{-1}}\). The fractional change in the density of glycerine for a rise of \(40^\circ \text{C}\) in its temperature is:$\mathrm{}$
1. \(0.015\)
2. \(0.020\)
3. \(0.025\)
4. \(0.010\)

The heart of a man pumps \(5~\text{L}\) of blood through the arteries per minute at a pressure of \(150~\text{mm}\) of mercury. If the density of mercury is \(13.6\times10^{3}~\text{kg/m}^{3}\)$$ $\mathrm{and}{\mathrm{}}^{}$ \(g = 10~\text{m/s}^2\), then the power of the heart in watt is:
1. \(1.70\)
2. \(2.35\)
3. \(3.0\)
4. \(1.50\)